The symmetry origin of the austenite-cementite orientation relationships in steels

The connection between austenite/cementite orientation relationships and crystal structure of both phases has been established. The nucleus formation mechanism at the mutual transformation of austenite and cementite structures has been proposed. Mechanism is based on the interpretation of the considered structures as crystallographic tiling onto triangulated polyhedra, and the said tiling can be transformed by diagonal flipping in a rhombus consisting of two adjacent triangular faces. The sequence of diagonal flipping in the fragment of the initial crystal determines the orientation of the fragment of the final crystal relative to the initial crystal. In case of the mutual austenite/cementite transformation the mutual orientation of the initial and final fragments is coinciding to the experimentally observed in steels Thomson-Howell orientation relationships: ${\left\{ {\bar 103} \right\}_{\rm{C}}}||{\left\{ {111} \right\}_{\rm{A}}};{\rm{}} < {\kern 1pt} 010{\kern 1pt} { > _{\rm{C}}}{\rm{||}} < {\kern 1pt} 10\bar 1{\kern 1pt} { > _{\rm{A}}};\; < {\kern 1pt} 30\bar 1{\kern 1pt} { > _{\rm{C}}}\;||\,\, < {\kern 1pt} \bar 12\bar 1{\kern 1pt} { > _{\rm{A}}}{\rm{}}$ The observed orientation relationship between FCC austenite and cementite is determined by crystallographic group-subgroup relationship between transformation participants, and non-crystallographic symmetry which is determining the transformation of triangulated clusters of transformation participants.